Case 2 Introduction In the production of rebars, carbon steel is melted down thr

ID: 340023 • Letter: C

Question

Case 2 Introduction In the production of rebars, carbon steel is melted down through a furnace, is molded and elongated into very hot rods, and are then pushed through the rolling mills which determines the sizes and lengths of the bars as appropriate. The annual demand for Carbon steel is 40,000 pounds. Its ordering cost is $ 30.00 while it’s holding cost is 20% per unit per year of the price of Carbon Steel. Carbon steel are sold at discounted prices as follows: Quantity range Cost (C) Less than 2500 pounds $ 0 .20 per pound 2500 to 5000 pounds $ 0.19 per pound 5000 or more pounds $ 0.18 per pound Which quantity should be ordered and at what cost?

Explanation / Answer

Following are the data provided :

Annual demand of carbon steel = D = 40,000 Pounds

Ordering cost = Co = $ 30

Annual unit holding cost = Ch = 20% of unit price

There will be different annual unit inventory holding costs for different quantity slabs and corresponding price levels

Accordingly, Economic order quantity ( EOQ ) which minimizes annual ordering cost plus annual inventory holding cost = Square root ( 2 x Co x D/ Ch )

Following table presents different values of Ch and their corresponding values of EOQ for various quantity slabs :

Quantity slab

Price ( $/ Pound )

Ch ( 20% of price)

EOQ ( rounded to nearest whole number )

Less than 2500

0.20

0.04

7746

2500 to 5000

0.19

0.038

7947

5000 or more

0.18

0.036

8165

It is only EOQ of 8165 which matches with its quantity slab of 5000 or more.

Therefore , EOQ = 8165 pounds

At EOQ = 8165 Pounds :

Annual purchasing cost = Annual demand x Price / unit = 40,000 x 0.18 = $7200

Annual ordering cost = Co x annual demand/EOQ = $ 30 x 40,000/8165 = $146.97

Annual inventory holding cost = Ch x average inventory = 0.036 x 8165/2 = $146.97

Total cost = $7200 + $146.97 + $146.97 = $7793.94